Question

In the given figure, if AC = 8 cm, DQ = 4 cm, and BP = 6 cm, find the area (cm${}^2$) of the quadrilateral ABCD.

Answer 1

Area of the quadrilateral ABCD = Area of $\Delta$ABC + Area of $\Delta$ACD

Area of the quadrilateral ABCD = $\frac{1}{2}\times AC\times BP$ + $\frac{1}{2}\times AC\times DQ$

Area of the quadrilateral ABCD = $\frac{1}{2}\times 8\times 6$ + $\frac{1}{2}\times 8\times 4$
Area of the quadrilateral ABCD = 24 + 16
Area of the quadrilateral ABCD = 40 cm${}^2$